1))))))))The average weight of a bag of dog biscuits produced by the Good Pet

Company is 10 kg with a standard deviation of 0.89 kg. A random sample of 48 bags was chosen from the production line.

a What type of distribution do you believe the sampling mean will follow (explain briefly to support your argument) and what are the

mean and standard deviation of this distribution?

b What is the probability that the sample mean weight will be more

than10.4kg?

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2))))))))))The general manager of a digital products manufacturer believes that 65%

of all potential customers prefer to buy MP3 players with over 2GB built-

in memory. A random sample of 100 customers was chosen.

a If the general manager’s belief is true, what is the standard deviation

of the sample proportion of customers that prefer to buy MP3 players with over 2GB built-in memory?

b If the general manager’s belief is true, what is the probability that the sample proportion of customers that prefer to buy MP3 players with over 2GB built-in memory is less than 0.75?

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3)))))))))))))))The marketing director of a comestic corporation wishes to estimate the average monthly demand for a newly released night-cream. She claims that the average monthly demand for the night-cream should be more than 4000. She is going to perform a survey in order to test her claim. The result of the survey will be used to determine the monthly quantity to be produced in order to satisfy the corresponding demand.

a State the null and alternative hypothesis for the above situation. Then explain the relevant meaning of Type I and Type II errors.

b Which type of error would be more significant if the stock carrying

cost is relatively lower than the out-of-stock cost? Explain briefly.

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4)))))))))))))))The chief executive officer of a large corporation has recently received complaints from quite a few employees, saying that there has been unfair treatment concerning workload between male staff and female staff.

Those employees claim that at least 60% of all the employees in the corporation have the same view. To verify the claim, 45 employees are randomly selected. Twenty-five of them expressed the view that there has been unfair treatment concerning workload between male staff and

female staff.

a Test whether the claim of those employees is justified or not usinga= 0.01 .

b Use thep-value approach to test the hypothesis at the same level of significance.